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Random Geometric Graphs$
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Mathew Penrose

Print publication date: 2003

Print ISBN-13: 9780198506263

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198506263.001.0001

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Random Geometric Graphs

Mathew Penrose (Contributor Webpage)

Oxford University Press

This introductory chapter contains a general discussion of both the historical and the applied background behind the study of random geometric graphs. A brief overview is presented, along with some standard definitions in graph theory and probability theory. Specific terminology is introduced for two limiting regimes in the choice of r=r(n) (namely the thermodynamic limit where the mean vertex degree is made to approach a finite constant) and the connectivity regime (where it grows logarithmically with n). Some elementary probabilistic results are given on large deviations for the binomial and Poisson distribution, and on Poisson point processes.

Keywords:   graph theory, Poisson process, binomial distribution, Poisson distribution, large deviations, thermodynamic limit, connectivity regime

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